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Question

If the equation x43x3+mx27x+3=0 has four positive real roots. Then,

A
the value of m should always be less than zero.
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B
the value of m should be zero
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C
the value of m should always be greater than zero.
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D
None of these
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Solution

The correct option is C the value of m should always be greater than zero.

The given equation is x43x3+mx27x+3=0

According to the relation between roots and coefficients of higher degree equations,
Sum of the roots taken two at a time

αβ=m

Since all the roots are positive real numbers

m should also be positive

So, m > 0.


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